a, b, c are positive integers forming an increasing geometric sequence, ba is a perfect square and log a +

log b + log c = 3. Find a + b + c.

Question

a, b, c are positive integers forming an increasing geometric
sequence, ba is a perfect square and log a +
log b + log c = 3 Find a + b + c

Anuradha Sharma · Accepted Answer

Since a, b, c are in GP, b2=actaking log we get, 2logb=loga+logc
1Now it is given loga+logb+logc=3
2So from equation 1 and 2, 2logb=3-logb3logb=3logb=1So b =10Now using equation 2, logabc=3abc=103=100or ac=100So only possibility for inclreasing GP is 5×20So a=5, b=10, c=20So a+b+c=35

a, b, c are positive integers forming an increasing geometric sequence, ba is a perfect square and log a + log b + log c = 3. Find a + b + c.

a, b, c are positive integers forming an increasing geometric sequence, ba is a perfect square and log a +

log b + log c = 3. Find a + b + c.